Riemann Surface for Square Root z^2-1 Picture.

Riemann Surface for (z²-1)^1/2. This surface is an object in four dimensions and cannot be drawn properly in three dimensions. The self intersections that the picture shows are a by-product of projecting the surface on three dimensions. The singularities in the surface are at the branch points, namely: at z=1 and at z=-1.

Picture obtained using the script RiemannSur in the Athena 18.04 MatLab Toolkit.

Riemann Surfaces: f(z) = (z²-1)^1/2.	Back:

Riemann Surface for (z²-1)^1/2. This surface is an object in four dimensions and cannot be drawn properly in three dimensions. The self intersections that the picture shows are a by-product of projecting the surface on three dimensions. The singularities in the surface are at the branch points, namely: at z=1 and at z=-1. Picture obtained using the script RiemannSur in the Athena 18.04 MatLab Toolkit.	Back: